2024 IMO Problems/Problem 4
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Let ABC be a triangle with AB < AC < BC. Let the incentre and incircle of triangle ABC be I and ω, respectively. Let X be the point on line BC different from C such that the line through X parallel to AC is tangent to ω. Similarly, let Y be the point on line BC different from B such that the line through Y parallel to AB is tangent to ω. Let AI intersect the circumcircle of triangle ABC again at P ̸= A. Let K and L be the midpoints of AC and AB, respectively. Prove that ∠KIL + ∠Y P X = 180◦ .
